iMessages won't sync to iCloud on Mac

I'm running Sonoma 14.2.1 on my iMac and cannot enable iCloud syncing of iMessages. I have an iPhone and an iPad which both use iCloud for iMessages and sync with one another fine. I can send and receive iMessages on the Mac, just not sync to iCloud or the other devices.

In System Settings / Apple ID / iCloud / "Apps using iCloud" / Messages, I have "Use on this Mac" turned on, but for "in iCloud" it says "0 messages" and the Status is "Not synced"; clicking "Sync now" has no effect.

In Messages / Settings / iMessage, the "Enable Messages in iCloud" option is missing and there is no "Sync now" button.

I tried resetting things by signing out of my Apple ID in Messages and turning off "Messages in iCloud" in System Settings, then deleting the following items, followed by a trash empty and restart:

~/Library/Messages

~/Library/Preferences/com.apple.imessage.plist

~/Library/Preferences/com.apple.imessage.bag.plist

Unfortunately, this had no effect.

Any help would be appreciated.

Mark